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Theorem suctrALTcf 29108
 Description: The sucessor of a transitive class is transitive. suctrALTcf 29108, using conventional notation, was translated from virtual deduction form, suctrALTcfVD 29109, using a translation program. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
suctrALTcf

Proof of Theorem suctrALTcf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 sssucid 4661 . . . . . . . 8
2 id 21 . . . . . . . . 9
3 id 21 . . . . . . . . . 10
4 simpl 445 . . . . . . . . . 10
53, 4syl 16 . . . . . . . . 9
6 id 21 . . . . . . . . 9
7 trel 4312 . . . . . . . . . 10
873impib 1152 . . . . . . . . 9
92, 5, 6, 8syl3an 1227 . . . . . . . 8
10 ssel2 3345 . . . . . . . 8
111, 9, 10eel0321old 28900 . . . . . . 7
12113expia 1156 . . . . . 6
13 id 21 . . . . . . . . 9
14 eleq2 2499 . . . . . . . . . 10
1514biimpac 474 . . . . . . . . 9
165, 13, 15syl2an 465 . . . . . . . 8
171, 16, 10eel021old 28875 . . . . . . 7
1817ex 425 . . . . . 6
19 simpr 449 . . . . . . . 8
203, 19syl 16 . . . . . . 7
21 elsuci 4650 . . . . . . 7
2220, 21syl 16 . . . . . 6
23 jao 500 . . . . . . 7
24233imp 1148 . . . . . 6
2512, 18, 22, 24eel2122old 28902 . . . . 5
2625ex 425 . . . 4
2726alrimivv 1643 . . 3
28 dftr2 4307 . . . 4
2928biimpri 199 . . 3
3027, 29syl 16 . 2
3130iin1 28737 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 359   wa 360  wal 1550   wceq 1653   wcel 1726   wss 3322   wtr 4305   csuc 4586 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-un 3327  df-in 3329  df-ss 3336  df-sn 3822  df-uni 4018  df-tr 4306  df-suc 4590
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